The Support Vector Machine(SVM) is a popular classification algorithm, however, it suffers from the drawback that the classification time for an unknown data point is proportional to the number of support vectors (SVs). Thus, its application for real-time decision-making, especially for complex class boundaries becomes problematic/impossible. In this article, we propose an algorithm, Self-Organizing Support Vector Machine(SO-SVM), which can decrease the number of SVs without compromising the accuracy. In this algorithm, we first cluster the data points using self-organizing map to find potential class boundary points, which are crucial for determining the separating hyperplane in an SVM. The separating hyperplane is then learned from the selected boundary points, leading to a reduction in the number of SVs. Learning the SVM also becomes efficient because of the reduced number of data points. The proposed algorithm has been tested on a number of benchmark datasets and found to decrease the number of SVs without deteriorating the classification accuracy. The SO-SVM algorithm thus can be an efficient alternative to the SVM algorithm and thus can be applied instead of normal SVM without making a noticeable compromise with the performance.